I heard from a number of Syrian refugees that this is actually very common in countries like theirs, where births may not be recorded, records are lost or destroyed. Some people don't even know their exact date of birth and they would typically enter January 1st on forms like this too.

A common case even in stable, industrialised, first-world nations. Bottom line, it’s a false assumption that everyone knows the date or even year of their birth, quite apart from being willing to disclose it or able to prove it.

I can also reveal that parents routinely mix up the DoB of their kids, and the more kids they have the worse this becomes, and I realised at some point during my association with club-level sport that it is a direct consequence of how tired they are